Solution - Base conversion

724

724

Step-by-step explanation

${(2 D 4)}_{16} = b a s e 10$

Identify the source number, source base, and target base before converting through base 10.

${(2 D 4)}_{16} = 2 \cdot 16^{2} + 13 \cdot 16^{1} + 4 \cdot 16^{0}$

$2 \cdot 16^{2} + 13 \cdot 16^{1} + 4 \cdot 16^{0} = 724$

Expand each digit by place value: $2 \cdot 16^{2}$
+ $13 \cdot 16^{1}$
+ $4 \cdot 16^{0}$ . This gives $724$ in base 10.

$\frac{724}{10} = 72 r e m a \in d e r 4$

$\frac{72}{10} = 7 r e m a \in d e r 2$

$\frac{7}{10} = 0 r e m a \in d e r 7$

$4 \to 2 \to 7 = 724$

$724 (b a s e 10) = {(724)}_{10}$

Repeatedly divide $724$ by $10$ , collect remainders, and read them in reverse to get $724$ .

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Base conversion is foundational for computer science, digital systems, and number theory.